Light from a point source in air falls on spherical glass surface ( \(n=1.5\) and radius of curvature \(=20 \mathrm{~cm}\) ). The distance of the light source from the glass surface is 100 cm . Find the image distance.

A -100 cm
B -200 cm
C 200 cm
D 100 cm

Verified Solution

Answer & Solution

Correct Answer

(D) 100 cm

Step-by-step Solution

Detailed explanation

(D) 100 cn
\(R=+20 \mathrm{~cm}\)
\(n_{1}=1 \quad n_{2}=1.5\)
\(u=-100 \mathrm{~cm} \quad v=\) ?
\(
\begin{array}{rlrl}
& & \frac{n_{2}}{v}-\frac{n_{1}}{u} & =\frac{n_{2}-n_{1}}{R} \\
& \therefore & \frac{1.5}{v}-\frac{1}{-100} & =\frac{1.5-1}{20} \\
& \therefore & \frac{1.5}{v}+\frac{1}{100} & =\frac{0.5}{20} \\
& \therefore & & \frac{1.5}{v} \\
& = & \frac{0.5}{20}-\frac{1}{100} \\
& \therefore & & \frac{1.5}{v} \\
& = & \frac{2.5-1}{100} \\
& \therefore & & \frac{1.5}{v} \\
& \therefore & & =\frac{1.5}{100} \\
& = & v & =+100 \mathrm{~cm}
\end{array}
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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